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Grade: 12th pass
        prove that root 3 is irrational number?
3 years ago

Answers : (4)

Vikas TU
11142 Points
							
Suppose assume root3 is a rational number.
Then
root(3) can be expressed as: = p/q
where p,q are the integers.
then write,
p =qroot3
squaring both sides,
p^2 = 3q^2
 
Now for any integer (p,q)
the eqn. is not going to satify.
Therfore from the contradiction it gets untrue.
Hence it is not a rational number then therfore, it is a irrational number.
3 years ago
BHOOPELLY SAIKUMAR
19 Points
							
prove that for all p,q that equation not satisfies.
and send post the answer . need proof for that,
how do I conclude that is not going to satisfy by directly telling so just post it
 
3 years ago
BHOOPELLY SAIKUMAR
19 Points
							
WE NEED TO PROVE THAT  FOR ALL P,Q SUCH THAT P2=3Q2 DOESN’T EXIST WHERE P,Q BELONGS TO Z. so justify ur answer with proper reason ….
3 years ago
mycroft holmes
272 Points
							
P and Q are natural numbers, and hence in the prime factorization of P2 and Q2, every prime factor appears to an even power.
 
Now in the equation P2=3Q2 we have a contradiction as LHS has an even exponent for 3, whereas on RHS exponent of 3 is odd. So no such pair (P,Q) exists.
 
Hence \sqrt 3 is irrational
3 years ago
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